This work will derive the full range of solutions for the six DSW types which arise as solutions of the equations governing
optical beam propagation in the nonlinear optical medium of a nematic liquid crystal [1]}, [2]}, [3]}. The equations
governing optical beam propagation in a nematic liquid crystal consist of an NLS-type equation for the electric field of
the optical beam and an elliptic equation for the nematic response. Previous studies [4]}, [5]} have found
that linear radiation can be in resonance with the waves of the DSW if the initial beam has a strong enough intensity
discontinuity, with a resonant wavetrain propagating ahead of the main DSW. Again, if the intensity jump is large enough,
a DSW as such does not occur, with a resonant wavetrain dominating the solution, as for the Kawahara equation (REF )
[6]}. These previous studies did not give satisfactory agreement with numerical solutions of the nematic equations
over the full range of intensity jump strengths. The only good agreement was obtained for the so-called dam break case for which
the optical intensity rises from 0 and the solution consists of an expansion wave with no DSW structure [4]}. The
reason that good agreement between theoretical and numerical solutions was not obtained for the other cases is that the first
study [4]} assumed that the solution was of KdV DSW-type for all the other five regimes, while the second study
[5]} assumed that the solution always has a gas dynamic shock structure for all these five regimes. It is found here
that these two assumptions do not hold over all solution regimes. The DSW is only of (perturbed) KdV-type for small initial
intensity jumps. As the initial optical intensity jump increases, the solution structure changes to the previously mentioned
strong resonant wavetrain terminated by a Whitham shock. This is not the same as the shock structure assumed by
[5]} as this work assumed that the shock was a non-dispersive shallow water equation type shock. It is found
here that this approximation is not satisfactory as the full Whitham shock, including dispersion, has to be used
to construct the solution in this regime. In addition to these two limiting cases for small and large initial intensity jumps,
the solution for the transition regime between these two limits will be constructed.
